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Polycrystalline Perovskite Ferroelectrics: Microstructural Origins of the Macroscale Electromechanical Response
Get PDFFerroelectrics are a class of electromechanically coupled materials which possess an electric dipole polarization that can be permanently reoriented by applied electric and mechanical stress fields. Their reorientable polarization results in complex, nano- to micrometer scale domain structures whose evolution under electric and mechanical stress fields alters the material's overall time-dependent electrical and viscoelastic properties. To understand domain structure evolution, in-situ microscopy of domain switching processes in ferroelectric thin films, single crystals and nanoparticles have been well-studied in the past. However, domain evolution in bulk polycrystals is less well understood as their local stress and electric field environment differs from thin specimens.
This work seeks to understand ferroelectric domain evolution in bulk ferroelectric perovskite polycrystals using a combination of a recently-developed electromechanical characterization technique, Broadband Electromechanical Spectroscopy (BES), and theoretical-computational predictions. A constitutive material model for polycrystalline ferroelectrics is first developed and applied to simulate barium titanate single crystals and polycrystals. Simulated polarization, strain and energy dissipation hysteresis curves show good qualitative agreement to experimental data and demonstrate that macroscale properties can be efficiently predicted from microscale physics to some extent.
The microstructural origins of fatigue behavior in bulk polycrystalline lead zirconate titanate (PZT) are investigated using a combination of macroscale electrical and viscoelastic property characterization via BES, and scanning electron microscopy (SEM) imaging of microstructure. The evolution of electrical and viscoelastic properties during bipolar electrical fatigue show differences in the effects of electrical vs. mechanical fatigue processes, and the latter is verified through SEM imaging and measurement of microcracks.
Finally, the same electromechanical BES characterizations are performed on specimens of bulk polycrystalline barium titanate (BT). Results reveal stark qualitative differences in electrical and viscoelastic responses from PZT despite both materials being perovskite ferroelectrics. A growth vs. nucleation hypothesis is proposed to explain the observed results, guided by preliminary imaging of domain microstructure.
In summary, the BES is a powerful tool to elucidate domain switching processes within bulk ferroelectric specimens, while a computational method which bridges the micro- and macroscale further adds to the diagnostic toolbox of understanding bulk ferroelectric domain switching mechanisms. This opens the pathway to designing future applications which make use of the unique electrical and viscoelastic properties of ferroelectric switching.</p
Imprints of Massive Scalars on Primordial Non-Gaussianities
Get PDFIn this thesis, we modify the standard single-field inflation scenario by adding additional massive scalars to the inflationary field content. Due to the breaking of time translational invariance by the inflaton background, the inflaton can interact with these extra scalars through a kinetic mixing term. If these scalars have self- interactions, then their kinetic mixings with the inflaton induce potentially large primordial non-gaussianities in the scalar curvature fluctuations, which could be observed in the cosmic microwave background (CMB) and large-scale structure (LSS). We derive expressions for these non-Gaussianities in the limits the scalar masses are much larger than or much smaller than the Hubble constant during inflation and compute their contributions to dark matter halo correlation functions.</p
Modeling, Computation, and Characterization to Accelerate the Development of Synthetic Gene Circuits in Cell-Free Extracts
Get PDFSynthetic biology may be defined as an attempt at using engineering principles to design and build novel biological functionalities. An important class of such functionalities involves the bottom up design of genetic networks (or 'circuits') to control cellular behavior. Performing design iterations on these circuits in vivo is often a time consuming process. One approach that has been developed to address these long design times is to use E. coli cell extracts as simplified circuit prototyping environments. The analogy with similar approaches in engineering, such as prototyping using wind tunnels and breadboards, may be extended by developing accompanying computer aided design tools. In this thesis, we discuss the development of computational and mathematical tools to accelerate circuit prototyping in the TX-TL cell free prototyping platform, and demonstrate some applications of these tools.
We start by discussing the problem of reducing circuit behavior variability between different batches of TX-TL cell extracts. To this end, we demonstrate a model-based methodology for calibrating extract batches, and for using the calibrations to 'correct' the behavior of genetic circuits between batches. We also look at the interaction of this methodology with the phenomenon of parameter non-identifiability, which occurs when the parameter identification inverse problem has multiple solutions. In particular, we derive conditions under which parameter non-identifiability does not hinder our modeling objectives, and subsequently demonstrate the use of such non-identifiable models in performing data variability reduction.
Next, we describe txtlsim, a MATLAB Simbiology based toolbox for automatically generating models of genetic circuits in TX-TL, and for using these models for part characterization and circuit behavior prediction. Large genetic circuits can have non-negligible resource usage needs, leading to unintended interactions between circuit nodes arising due to the loading of cellular machinery, transcription factors or other regulatory elements. The usage of consumable resources like nucleotides and amino acids can also have non-trivial effects on complex genetic circuits. These types of effects are handled by the modeling framework of txtlsim in a natural way.
We also highlight mcmc-simbio, a smaller toolbox within txtlsim for performing concurrent Bayesian parameter inference on Simbiology models. Concurrent inference here means that a common set of parameters can be identified using data from an ensemble of different circuits and experiments, with each experiment informing a subset of the parameters. The combination of the concurrence feature with the fact that Markov chain Monte Carlo based Bayesian inference methods allow for the direct visualization of parameter non-identifiability enables the design of ensembles of experiments that reduce such non-identifiability.
Finally, we end with a method for performing model order reduction on transcription and translation elongation models while maintaining the ability of these models to track resource consumption. We show that due to their network topology, our models cannot be brought into the two-timescale form of singular perturbation theory when written in species concentration coordinates. We identify a coordinate system in which singular perturbation theory may be applied to chemical reaction networks more naturally, and use this to achieve the desired model reduction.</p
Synthetic Strategies for the Total Synthesis of Acutumine Alkaloids and the Development of Radical Deoxychlorination Reactions
Get PDFThe acutumine alkaloids are a family of architecturally complex propellane natural products with promising medicinal properties. Herein, we disclose the continued development of a synthetic strategy toward the asymmetric total synthesis of acutumine alkaloids. The spirocyclic scaffold was synthesized in two new series, which follow our successful access to the dechloroacutumine core in 2013. Central to the synthetic design is the retro-aldol/Dieckmann cyclization of a cyclobutyl lactone to install the spirocycle. The key cyclobutane intermediate is obtained via a photo-mediated [2+2]-cycloaddition of a furanyl dihydroindolone, which is accessible via a stereoselective 1,2-addition/reductive cyclization sequence of a benzoquinone-derived imine. Installation of the dimethoxyenone motif is accomplished via a late-stage elimination of a dimethoxyketal, which furnished the requisite vinylogous ester after methylation. Overall, these efforts have culminated in the synthesis of the complete carbocyclic core and oxidation pattern of the natural product (–)-acutuminine, with a C10 neopentyl alcohol in place of the neopentyl chloride.
Ten of the known acutumine alkaloids contain a neopentyl chloride; this motif provided underlying motivation for the development of novel radical deoxychlorination reactions, including the chlorination of cesium oxalates. This reaction allows access to hindered 2° and 3° alkyl chlorides, provides complementary reactivity to standard heterolytic conditions, and is performed under mild conditions using visible light and ethyl trichloroacetate as a Cl• source. Application to deoxybromination and deoxyfluorination is also demonstrated, showcasing the versatility of the discovered halogenation. This method should find broad utility in the deoxyhalogenation of hindered alcohols, particularly in the pharmaceutical industry where selective installation of fluorides is a common challenge.</p
Time-Varying Optimization and Its Application to Power System Operation
Get PDFThe main topic of this thesis is time-varying optimization, which studies algorithms that can track optimal trajectories of optimization problems that evolve with time. A typical time-varying optimization algorithm is implemented in a running fashion in the sense that the underlying optimization problem is updated during the iterations of the algorithm, and is especially suitable for optimizing large-scale fast varying systems. Motivated by applications in power system operation, we propose and analyze first-order and second-order running algorithms for time-varying nonconvex optimization problems.
The first-order algorithm we propose is the regularized proximal primal-dual gradient algorithm, and we develop a comprehensive theory on its tracking performance. Specifically, we provide analytical results in terms of tracking a KKT point, and derive bounds for the tracking error defined as the distance between the algorithmic iterates and a KKT trajectory. We then provide sufficient conditions under which there exists a set of algorithmic parameters that guarantee that the tracking error bound holds. Qualitatively, the sufficient conditions for the existence of feasible parameters suggest that the problem should be "sufficiently convex" around a KKT trajectory to overcome the nonlinearity of the nonconvex constraints. The study of feasible algorithmic parameters motivates us to analyze the continuous-time limit of the discrete-time algorithm, which we formulate as a system of differential inclusions; results on its tracking performance as well as feasible and optimal algorithmic parameters are also derived. Finally, we derive conditions under which the KKT points for a given time instant will always be isolated so that bifurcations or merging of KKT trajectories do not happen.
The second-order algorithms we develop are approximate Newton methods that incorporate second-order information. We first propose the approximate Newton method for a special case where there are no explicit inequality or equality constraints. It is shown that good estimation of second-order information is important for achieving satisfactory tracking performance. We also propose a specific version of the approximate Newton method based on L-BFGS-B that handles box constraints. Then, we propose two variants of the approximate Newton method that handle explicit inequality and equality constraints. The first variant employs penalty functions to obtain a modified version of the original problem, so that the approximate Newton method for the special case can be applied. The second variant can be viewed as an extension of the sequential quadratic program in the time-varying setting.
Finally, we discuss application of the proposed algorithms to power system operation. We formulate the time-varying optimal power flow problem, and introduce partition of the decision variables that enables us to model the power system by an implicit power flow map. The implicit power flow map allows us to incorporate real-time feedback measurements naturally in the algorithm. The use of real-time feedback measurement is a central idea in real-time optimal power flow algorithms, as it helps reduce the computation burden and potentially improve robustness against model mismatch. We then present in detail two real-time optimal power flow algorithms, one based on the regularized proximal primal-dual gradient algorithm, and the other based on the approximate Newton method with the penalty approach
Phonon Dynamics and Damping in Three-Dimensional Acoustic Bandgap Cavity-Optomechanical Resonators
Get PDFMechanical resonators are used in a wide variety of technical applications, from precision time keeping and sensing, to the delay and filtering of microwave signals in mobile communication systems. Critical to many of these applications is the ability of a mechanical object to store vibrational energy at a well defined frequency of oscillation and with minimal damping. Energy damping can occur through acoustic radiation into the resonator support structure, or through impurities and defects in the resonator material, and is highly dependent on the temperature of operation due to the inherent anharmonic motion of atoms within solid-state materials. Here, we present optical measurements down to milliKelvin temperatures of the acoustic mode properties of a crystalline silicon nanobeam cavity incorporating a three-dimensional phononic bandgap support structure for acoustic confinement. Utilizing pulsed laser light to excite a co-localized optical mode of the optomechanical crystal (OMC) device, we are able to measure the dynamics of the internal cavity acoustic modes which are coupled to the light field via radiation pressure. These measurements represent an almost ideal scenario in which the ringdown occurs free of any additional mechanical or probe field contact, and where elastic scattering or radiation of the acoustic field does not lead to energy damping due to the full bandgap shield. The resulting ringdown measurements for the fundamental 5 GHz acoustic mode of the cavity show an exponential increase in phonon lifetime versus phononic shield period number, which at a bath temperature of 35 milliKelvin saturates above six periods to a value as long as 1.5 seconds. This ultra-long lifetime, corresponding to an effective phonon propagation length of several kilometers, is found at the lowest temperatures to be consistent with damping from non-resonant tunneling states whose energy lies below the acoustic shield phononic bandgap, and which are most likely present in the amorphous etch-damaged region of the silicon surface. Other, more rapid forms of damping such as resonant tunneling state damping or three-phonon scattering are suppressed due to the phononic bandgap shield and the reduced density of phonon states in the effectively one-dimensional nanobeam geometry. Prospects for newapplications of ultra-coherent nanoscale mechanical resonators include tests of various collapse models of quantum mechanics, or, if appropriately integrated with microwave superconducting quantum circuits, as miniature quantum memory or processing units with potentially many-orders of magnitude longer coherence time than their electromagnetic counterparts.</p
Sparse Deconvolution with Applications to Spike Sorting
Get PDFChronic extracellular recording is the use of implanted electrodes to measure the electrical activity of nearby neurons over a long period of time. It presents an unparalleled view of neural activity over a broad range of time scales, offering sub-millisecond resolution of single action potentials while also allowing for continuous recording over the course of many months. These recordings pick up a rich collection of neural phenomena -- spikes, ripples, and theta oscillations, to name a few -- that can elucidate the activity of individual neurons and local circuits.
However, this also presents an interesting challenge for data analysis. Chronic extracellular recordings contain overlapping signals from multiple sources, requiring these signals to be detected and classified before they can be properly analyzed. The combination of fine temporal resolution with long recording durations produces large datasets, requiring efficient algorithms that can operate at scale.
In this thesis, I consider the problem of spike sorting: detecting spikes (the extracellular signatures of individual neurons' action potentials) and clustering them according to their putative source. First, I introduce a sparse deconvolution approach to spike detection, which seeks to detect spikes and represent them as the linear combination of basis waveforms. This approach is able to separate overlapping spikes without the need for source templates, and produces an output that can be used with a variety of clustering algorithms.
Second, I introduce a clustering algorithm based around a mixture of drifting t-distributions. This model captures two features of chronic extracellular recordings -- cluster drift over time and heavy-tailed residuals in the distribution of spikes -- that are missing from previous models. This enables us to reliably track individual neurons over longer periods of time. I will also show that this model produces more accurate estimates of classification error, which is an important component to proper interpretation of the spike sorting output.
Finally, I present a few theoretical results that may assist in the efficient implementation of sparse deconvolution.</p
An Enhanced Maximum-Entropy Based Meshfree Method: Theory and Applications
Get PDFThis thesis develops an enhanced meshfree method based on the local maximum-entropy (max-ent) approximation and explores its applications. The proposed method offers an adaptive approximation that addresses the tensile instability which arises in updated-Lagrangian meshfree methods during severe, finite deformations. The proposed method achieves robust stability in the updated-Lagrangian setting and fully realizes the potential of meshfree methods in simulating large-deformation mechanics, as shown for benchmark problems of severe elastic and elastoplastic deformations. The improved local maximum-entropy approximation method is of a general construct and has a wide variety of applications. This thesis presents an extensive study of two applications - the modeling of equal-channel angular extrusion (ECAE) based on high-fidelity plasticity models, and the numerical relaxation of nonconvex energy potentials. In ECAE, the aforementioned enhanced maximum-entropy scheme allows the stable simulation of large deformations at the macroscale. This scheme is especially suitable for ECAE as the latter falls into the category of severe plastic deformation processes where simulations using mesh-based methods (e.g. the finite element method (FEM)) are limited due to severe mesh distortions. In the second application, the aforementioned max-ent meshfree method outperforms FEM and FFT-based schemes in numerical relaxation of nonconvex energy potentials, which is essential in discovering the effective response and associated energy-minimizing microstructures and patterns. The results from both of these applications show that the proposed method brings new possibilities to the subject of computational solid mechanics that are not within the reach of traditional mesh-based and meshfree methods.</p
Characterization of Adaptor Binding and Substrate Processing by VCP/p97
Get PDFValosin-containing protein (VCP/p97) is an essential AAA+ ATPase that is critical to numerous important cellular pathways, such as ER-associated degradation. p97 works in concert with a repertoire of adaptor proteins to extract ubiquitylated proteins from membranes or complexes and, often, target them for degradation by the protesome. The nature of the p97 system—dependent upon a complex network of accessory proteins and targeted to substrates that are unstable and heterogeneous—makes the mechanism of substrate processing challenging to study. Here, we developed in vitro biochemical assays to reconstitute two important steps in the p97 pathway for mechanistic study: adaptor binding and substrate processing. We showed that p97-adaptor complexes are highly dynamic, recapitulating observations made in cell lysate. Using a model p97 substrate, we demonstrated for the first time that p97 processes its substrates through unfolding, a fact long presumed but never explicitly proven. Finally, with these model systems in hand, we explored the effects of p97 mutations that cause the neurodegenerative disease multisystem proteinopathy (MSP) on p97-adaptor-substrate complexes. MSP mutations cause faster substrate unfolding, and we hypothesize that this increase is due to a higher affinity for the requisite adaptors Ufd1-Npl4. Our biochemical data presents evidence for a gain of function model for MSP pathology and suggests new avenues for treating MSP
Development of Nickel-Catalyzed Asymmetric Reductive Cross-Coupling Reactions
Get PDFAsymmetric reductive cross-electrophile coupling is a powerful method to forge C–C bonds and access enantioenriched small molecules, which can be further functionalized to access scaffolds present in natural products and bioactive pharmaceutical agents. However, an innate challenge of this methodology is identifying a chiral catalyst that achieves optimal cross-selectivity and stereocontrol. Herein, we report studies on the asymmetric cross-coupling of C(sp3) electrophiles, such as benzyl chlorides, α-chloroesters, and N-hydroxyphthalimide esters, with several classes of C(sp2) electrophiles.
We describe the asymmetric Ni-catalyzed reductive cross-coupling of (hetero)aryl iodides and benzyl chlorides to prepare enantioenriched 1,1-diarylalkanes. As part of these studies, a new chiral bi(oxazoline) ligand, 4-HeptylBiOX, was developed to obtain products in synthetically useful yield and enantioselectivity. This novel ligand is demonstrated to expand the substrate scope of these stereoconvergent reductive cross- couplings to include the asymmetric cross-coupling of α-chloroesters with aryl iodides, and sterically hindered N-hydroxyphthalimide esters with alkenyl bromides. Model studies have been initiated to study the application of these reactions toward the total synthesis of cylindrocyclophane natural products.</p